How to Calculate Percentage Change Between Two Numbers

Why Knowing How to Calculate Percentage Change Is Essential

How to calculate percentage change is one of the most practical arithmetic skills in everyday life. Whether you are comparing a stock price gain, a salary cut, year-over-year revenue, or your own weight-loss progress, the same formula applies every time. Miss it and you risk misreading data — or being misled by someone who presents numbers without the context of where they started.

Calculate any percentage change instantly with the free Percentage Calculator

Step 1: Identify the Original Value and the New Value

Before applying any formula, be precise about which number is "old" and which is "new."

• Original value (Old): the starting point, baseline, or earlier measurement
• New value (New): the ending point, result, or later measurement

Confusing the two is the most common source of errors. If a price was $45 last year and is $67 today, Old = $45 and New = $67.

Step 2: Subtract Old From New

Difference = New − Old

This step reveals the direction and raw magnitude of the change:

• A positive difference means an increase
• A negative difference means a decrease

Example: $67 − $45 = +$22 (increase)

Step 3: Divide by the Absolute Value of the Original

Ratio = Difference ÷ |Old|

Using the absolute value of Old matters when the original number is negative (rare but possible — for example, a company reporting a net loss that then swings to profit). For positive starting values, |Old| = Old.

Example: $22 ÷ $45 = 0.4889

Step 4: Multiply by 100

% Change = Ratio × 100

Example: 0.4889 × 100 = +48.9%

The complete formula:

% Change = ((New − Old) ÷ |Old|) × 100

Step 5: Add + or − Sign to Indicate Direction

Always include the sign. "+48.9%" and "−48.9%" are completely different outcomes. In professional contexts, a missing sign is ambiguous and potentially misleading.

Four real-world worked examples:

For quick work on any of these, the Percentage Calculator handles all four scenario types and also covers percentage-off discounts and inflation adjustments.

Common Scenarios With Numbers

5% raise on a $65,000 salary:

New = 65,000 × 1.05 = $68,250 % Change = (68,250 − 65,000) / 65,000 × 100 = +5.0%

15% price drop on a $200 item:

New = 200 × 0.85 = $170 % Change = (170 − 200) / 200 × 100 = −15.0%

25% revenue growth from $1.2M:

New = 1,200,000 × 1.25 = $1,500,000 % Change = (1.5M − 1.2M) / 1.2M × 100 = +25.0%

Checking a discount or an inflation adjustment? Both are specific applications of the same percentage change formula.

The Most Common Mistake: Percentage Change vs. Percentage Points

This distinction matters in finance, economics, and policy discussions.

If an interest rate rises from 3% to 5%:

• The change in percentage points is 5 − 3 = +2 percentage points
• The percentage change is (5 − 3) / 3 × 100 = +66.7%

A headline that reads "interest rates rose 2%" is ambiguous — it could mean either. "Rates rose 2 percentage points" and "rates rose 66.7%" both describe the same move, but they say very different things about magnitude.

The same applies to election polling, unemployment statistics, and test scores. When in doubt, ask: "2 what — percentage points, or a 2% relative change?"

Conclusion

Key takeaways:

• The formula is always: ((New − Old) ÷ |Old|) × 100
• Subtract first, then divide by the original, then multiply by 100
• Always include the + or − sign in your answer
• Percentage change and percentage point change are different concepts — especially relevant in finance and statistics
• Use the free Percentage Calculator for instant results without manual arithmetic